Least Common Multiple (LCM) of 126 and 53
The least common multiple (LCM) of 126 and 53 is 6678.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 126 and 53?
First, calculate the GCD of 126 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 53 = 2 remainder 20 |
| 2 | 53 ÷ 20 = 2 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 79 | 5451 |
| 35 and 197 | 6895 |
| 82 and 88 | 3608 |
| 159 and 192 | 10176 |
| 109 and 184 | 20056 |